Seamless image cloning by a closed form solution of a modified Poisson problem

A Poisson image editing is known as a seamless image cloning algorithm based on gradient field [Pérez et al. 2003]. The Poisson image editing is very effective algorithm and based on the Poisson equation. However, it is time consuming process to solve the Poisson equation. An approximated solution of the Poisson equation has been proposed to fasten the Poisson image editing [Farbman et al. 2009]. This approximated solution is computationally effective and can generate almost identical solution to the rigorous solution.